The rate of cooling (dropping of inside temperature) is going to be dependent on the differential between the outside temp and the inside temp. So if the outside temp is 20 degrees and the inside temp is 70 degrees (differential of 50 degrees), the rate at which it drops the inside temp will be faster than if the inside temp is at 50 degrees (differential of 30 degrees). Since the furnace will kick on when the temp drops 2-3 degrees below thermostat set point, it will cycle more at the higher temp. If the outside temp were 50 degrees, it would not cycle at all if set for 50 inside, whereas it would if set for 70.
Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).
